Hit the Cyclops in the chest 3 times with the spear. Then go to his fallen head and grapple it while wielding the spear. Only the spear holder can execute the Cyclops.
If your team has 7000 points or more when the execution begins, the game will play a victory cutscene for your team and end. If you have less than 7000 points, only the spear wielder will participate in the execution, and your team will receive 1000 points for the execution (not credited to any specific player.) The match will continue until the total of either team reaches 8000.
There is, however, a rare glitch that will give the other team your points for killing him.